Question

The number of integers in the domain of the function $f(x)=\sqrt{{\log }_{\frac{1}{2}}|x-2|+2}$ is

• A. 8
• B. 9
• C. 10
• D. more than 10

Answer 1

Answer: (A)

${\log }_{\frac{1}{2}}|x-2|\ge -2\Rightarrow |x-2|\le 4\Rightarrow -4\le x-2\le 4$
$-2\le x\le 6\Rightarrow \text{ Number of integers }=8(x\ne 2)$